论文标题
WZW模型通过当前代数变形的Poisson-lie T偶对性
Poisson-Lie T-Duality of WZW Model via Current Algebra Deformation
论文作者
论文摘要
Wess-Zumino-Witten（WZW）模型的Poisson-lie t偶（具有$ su（2）$的组歧管为目标空间。整个构建依赖于模型的仿射当前代数的变形，半主导总和$ \ Mathfrak {su}（2）（2）（\ Mathbb {r}）\，\ dot {\ dot {\ oplus} \，\ Mathfrak，\ mathfrak，\ Mathfrak {a} a} $ $ \ mathfrak {sl}（2，\ mathbb {c}）（\ mathbb {r}）$。获得了$ SL（2，\ Mathbb {C}）$的两参数模型家族作为目标相位空间，以便在相位空间中实现泊松lie t二维为$ O（3,3）$旋转。双重家族共享相同的相位空间，但其配置空间为$ sb（2，\ mathbb {c}）$，$ su（2）$的Poisson-lie dual。在$ sl（2，\ mathbb {c}）$上具有双倍自由度的父母动作，以及其Hamiltonian描述。
Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of $SU(2)$ as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct sum $\mathfrak{su}(2)(\mathbb{R}) \, \dot{\oplus} \, \mathfrak{a}$, to the fully semisimple Kac-Moody algebra $\mathfrak{sl}(2,\mathbb{C})(\mathbb{R})$. A two-parameter family of models with $SL(2,\mathbb{C})$ as target phase space is obtained so that Poisson-Lie T-duality is realised as an $O(3,3)$ rotation in the phase space. The dual family shares the same phase space but its configuration space is $SB(2,\mathbb{C})$, the Poisson-Lie dual of the group $SU(2)$. A parent action with doubled degrees of freedom on $SL(2,\mathbb{C})$ is defined, together with its Hamiltonian description.
